Multi-granular Evaluation Model Through Fuzzy Random Regression to Improve Information Granularity

  • Nureize Arbaiy
  • Junzo WatadaEmail author
Part of the Studies in Big Data book series (SBD, volume 8)


Extracting new information through regression analysis is somewhat difficult in environment which contains fuzzy and random situation; shows simultaneous uncertainty. Given this coexistence of random and fuzzy information, the data cannot be adequately treated by a conventional regression method. Thus, in this paper, a fuzzy random regression is introduced to improve the extraction of weight of granules in a multi-granular decision making. The proposed model will manage the multi-granular linguistic labels provided by evaluators in order to compute collective assessments about the product samples that will be used by the decision maker to determine final decision. The proposed model is applied to oil palm fruit grading, as the quality inspection process for fruits requires a method to ensure product quality. We include simulation results and highlight the advantage of the proposed method in handling the existence of fuzzy random information.


Fuzzy regression Multi-granular evaluation Fuzzy random regression 


  1. 1.
    Bargiela, A., Pedrycz, W.: Granular Computing. Kluwer, Dordrecht (2002)Google Scholar
  2. 2.
    Bargiela, A., Pedrycz, W.: Recursive information granulation. IEEETrans. SMC-B 33(1), 96–112 (2003)Google Scholar
  3. 3.
    Bargiela, A., Pedrycz, W.: Granular mappings. IEEE Trans. SMC A 35(2), 292–297 (2005)Google Scholar
  4. 4.
    Brans, J.P., Vincke, Ph, Mareschal, B.: How to rank and how to select projects: the PROMETHEE method. J. Oper. Res. 24(2), 228–238 (1986)CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Cardoso, D.M., de Sousa, J.F.: A multi-attribute ranking solutions confirmation procedure. Ann. Oper. Res. 138(1), 127–141 (2005)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    de Andres, R., Garcia-Lapresta, J.L., Martinez, L.: A multi-granular linguistic model for management decision-making in performance appraisal. Soft. Comput. 14(1), 21–34 (2010)CrossRefGoogle Scholar
  7. 7.
    Herrera, F., Martínez, L.: A model based on linguistic 2-tuples for dealing with multigranularity hierarchical linguistic contexts in multiexpert decision-making. IEEE Trans. Syst. Man Cybern. B Cybern. 31, 227–234 (2001)CrossRefGoogle Scholar
  8. 8.
    Keeney, R.L., Raiffa, H.: Decisions with Multi-objectives. Wiley, New York (1976)Google Scholar
  9. 9.
    Li, Y., Chen, S., Nie, X.: Fuzzy pattern recognition approach to construction contractor selection export. Fuzzy Optim. Decis. Making 4(2), 103–118 (2005)CrossRefzbMATHGoogle Scholar
  10. 10.
    Liu, B., Liu, Y.-K.: Expected value of fuzzy variable and fuzzy expected value models. IEEE Trans. Fuzzy Syst. 10(4), 445–450 (2002)CrossRefGoogle Scholar
  11. 11.
    Malczewski, J.: Propagation of errors in multicriteria location analysis: a case study. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making, Proceedings of the Twelfth International Conference, Hagen (Germany): 1995, Springer, Berlin, pp. 154–165 (1997)Google Scholar
  12. 12.
    MartLnez, L., Liu, J., Yang, J.B., Herrera, F.: A multi-granular hierarchical linguistic model for design evaluation based on safety and cost analysis. Int J Intell Syst 20, 1161–1194 (2005)CrossRefGoogle Scholar
  13. 13.
    Mavrotas, G., Diakoulaki, D., Capros, P.: Combined MCDA-IP approach for project selection in the electricity market. Ann. Oper. Res. 120(1–4), 159–170 (2003)CrossRefzbMATHMathSciNetGoogle Scholar
  14. 14.
    Meiarov, Z.: Granular computing and its application in Rbf neural network with cloud activation function. J. Inf. Control Manage. Syst. 7(1) (2009). Retrieved from
  15. 15.
    Nureize, A., Watada, J.: A fuzzy regression approach to hierarchical evaluation model for oil palm grading. Fuzzy Optim. Decis. Making 9(1), 105–122 (2010)CrossRefzbMATHGoogle Scholar
  16. 16.
    Nureize, A., Watada, J.: Multi-Attribute decision making in contractor selection under hybrid uncertainty. J. of Adv. Comput. Intelligence and Intell. Inf. 15(4), 465–472 (2010)Google Scholar
  17. 17.
    Nureize, A., Watada, J.: Fuzzy random regression based multi-attribute evaluation and its application to oil palm fruit grading. Ann. of Oper. Res. pp. 1-17 ( 2011). Doi:  10.1007/s10479-011-0979-z10.1007/s10479-011-0979-zTI
  18. 18.
    Ogryczak, W.: Multiple criteria linear programming model for portfolio selection. Ann. Oper. Res. 97(1), 143–162 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    Pedrycz, W. (ed.): Granular Computing: an Emerging Paradigm. Physica-Verlag, Heidelberg (2001)Google Scholar
  20. 20.
    Roy, A.: Classement et choix en prsence de points de vue multiples (la mthode ELECTRE). la Revue d’Informatique et de Recherche Oprationelle (RIRO), Vol. 8, pp. 57–75 (1968)Google Scholar
  21. 21.
    Saaty, T.L.: The Analytic Hierarchy Process. McGraw-Hill, New York (1980)zbMATHGoogle Scholar
  22. 22.
    Tanaka, H., Watada, J.: Possibilistic linear systems and their application to the linear regression model. Fuzzy Sets Syst. 27(3), 275–289 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  23. 23.
    Tanaka, H., Hayashi, I., Watada, J.: Possibilistic linear regression for fuzzy data. Eur. J. of Oper. Res. 40(3), 389–396 (1989)Google Scholar
  24. 24.
    Tavana, M., Sodenkamp, M.A., Suhl, L.: A soft multi-criteria decision analysis model with application to the European union enlargement. Ann. Oper. Res. 181(1), 393–421 (2010)CrossRefzbMATHMathSciNetGoogle Scholar
  25. 25.
    Watada, J., Tanaka, H.: Fuzzy Quantification Methods. In: Proceedings of the 2nd IFSA Congress, at Tokyo, 66–69 (1987)Google Scholar
  26. 26.
    Watada, J.: Trend of fuzzy multivariant analysis in management engineering. In: Khosla, R. et al. (eds.) KES2005, LNAI 3682, Springer, Berlin. pp. 1283–1290 (2005)Google Scholar
  27. 27.
    Watada, J., Toyoura, Y.: Formulation of fuzzy switching auto-regression model. Int. J. Chaos Theory Appl. 7(1, 2), 67–76 (2002)Google Scholar
  28. 28.
    Watada, J., Wang, S., Pedrycz, W.: Building confidence interval-based fuzzy random regression model. IEEE Trans. Fuzzy Syst. 11(6), 1273–1283 (2009)CrossRefGoogle Scholar
  29. 29.
    Yager, R.: On ordered weighted averaging aggregation operators in multi-criteria decision making. IEEE Trans. Syst. Man Cybern. 18(1), 183–190 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  30. 30.
    Yao, Y.Y.: A partition model of granular computing. LNCS Trans. Rough Sets 1, 232–253 (2004)Google Scholar
  31. 31.
    Yao, Y.Y.: Granular computing. Comput. Sci. (Ji Suan Ji Ke Xue) 31, 1–5 (2004)Google Scholar
  32. 32.
    Yao, Y.Y.: Perspectives of Granular Computing Proceedings of 2005 IEEE International Conference on Granular Computing, 1, pp. 85–90 (2005)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Faculty of Computer Science and Information TechnologyUniversity Tun Hussein Onn MalaysiaJohorMalaysia
  2. 2.Graduate School of Information, Production and SystemWaseda UniversityKitakyushuJapan

Personalised recommendations